Planning recessed spotlights/LED spots

Ceiling height 2.55, LED spots 8W 35-degree beam angle. However, I am open to anything. Surface will be a lime plaster

Thanks first of all for the additional data.
What is the CRI and the color temperature?
Dimmable?
In general, it is worth considering whether you need such an even illumination in the bathroom. Having the entire ceiling covered with spots in a grid does not really look good.
What IP rating do the spots have if you want to use them in the shower/bathroom as well?
Please mention the model of the spots. The volume flow can vary greatly even at 8 watts.
Without having calculated it, I would say that you will not achieve 300 L/m² in the bathroom. A beam angle of 35° is rather narrow already.

I've got my eye on the Osram Parathom PAR16. 2700K, dimmable.

As I said, I'm open to anything.

Ok, now it becomes clearer. You want to use LED bulbs in a GU10 socket. I was thinking of something different with LED recessed spotlights. To use these bulbs in a damp room or even in the shower area, the socket must have an appropriate sealing (IP rating). Have you already gotten some for testing? 2700k would be too yellowish for me personally. For example, take a look at the constaled from Voltus. They are also available with 60° beam angle and, above all, a better CRI value. The matching sockets are also available there.

ok thanks, I will take a look at it. What do I do now with my bathroom?

First, you need to get clear about the [Leuchten]. Then you can determine the positions and distances. If you have no time or desire to do the calculations yourself, there are some providers who will do this for you free of charge or for a small fee. If the result does not have to be 100% accurate, your current planning is certainly not wrong.